Dear Joe Tucciarone:
Thank you for posting on History Hub!
Even though there was no census in 1833, immigration data from individuals from the Italian peninsula could have been provided by border crossings, passenger lists, naturalizations, and other types of records. The document that you shared was created after the unification of Italy, so that is most likely why the U.S. Census Bureau is using the term “Italians”.
Here is an interesting State Department web page on the diplomatic relationship with the Italy peninsula before its unification.
Thanks for the information, James.